How do you tell if a relationship is proportional?

Video transcript

What I want to introduce you to in this video is the notion of a proportional relationship. And a proportional relationship between two variables is just a relationship where the ratio between the two variables is always going to be the same thing. So let's look at an example of that. So let's just say that we want to think about the relationship between x and y. And let's say that when x is one, y is three, and then when x is two, y is six. And when x is nine, y is 27. Now this is a proportional relationship. Why is that? Because the ratio between y and x is always the same thing. And actually the ratio between y and x or, you could say the ratio between x and y, is always the same thing. So, for example-- if we say the ratio y over x-- this is always equal to-- it could be three over one, which is just three. It could be six over two, which is also just three. It could be 27 over nine, which is also just three. So you see that y over x is always going to be equal to three, or at least in this table right over here. And so, or at least based on the data points we have just seen. So based on this, it looks like that we have a proportional relationship between y and x. So this one right over here is proportional. So given that, what's an example of relationships that are not proportional. Well those are fairly easy to construct. So let's say we had-- I'll do it with two different variables. So let's say we have a and b. And let's say when a is one, b is three. And when a is two, b is six. And when a is 10, b is 35. So here-- you might say look, look when a is one, b is three so the ratio b to a-- you could say b to a-- you could say well when b is three, a is one. Or when a is one, b is three. So three to one. And that's also the case when b is six, a is two. Or when a is two, b is six. So it's six to two. So these ratios seem to be the same. They're both three. But then all of sudden the ratio is different right over here. This is not equal to 35 over 10. So this is not a proportional relationship. In order to be proportional the ratio between the two variables always has to be the same. So this right over here-- This is not proportional. Not proportional. So the key in identifying a proportional relationship is look at the different values that the variables take on when one variable is one value, and then what is the other variable become? And then take the ratio between them. Here we took the ratio y to x, and you see y to x, or y divided by x-- the ratio of y to x is always going to be the same here so this is proportional. And you could actually gone the other way. You could have said, well what's the ratio of x to y? Well over here it would be one to three, which is the same thing as two to six, which is the same thing as nine to 27. When you take this ratio-- if you say the ratio of x to y instead of y to x, you see that it is always one third. But any way you look at it-- the ratio between these two variables-- if you say y to x, it's always going to be three. Or x to y is always going to be one third. So this is proportional while this one is not.

Popular Tutorials in Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

• What's a Proportion?

  The idea of proportions is that a ratio can be written in many ways and still be equal to the same value. That's why proportions are actually equations with equal ratios. This is a bit of a tricky definition, so make sure to watch the tutorial!

• How Do You Find Equivalent Ratios?

  Ratios are used to compare numbers. When you're working with ratios, it's sometimes easier to work with an equivalent ratio. Equivalent ratios have different numbers but represent the same relationship. In this tutorial, you'll see how to find equivalent ratios by first writing the given ratio as a fraction. Take a look!

• How Do You Know If Two Ratios are Proportional?

  Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional. To see this process in action, check out this tutorial!

• What are Equivalent Ratios?

  Equivalent ratios are just like equivalent fractions. If two ratios have the same value, then they are equivalent, even though they may look very different! In this tutorial, take a look at equivalent ratios and learn how to tell if you have equivalent ratios.

WHAT ARE PROPORTIONAL RELATIONSHIPS?

A relationship is proportional if each pair of data values are related in the same way, by multiplying by a factor. You can recognize a proportional relationship by looking at data, an equation, or a graph.

To better understand proportional relationships…

WHAT ARE PROPORTIONAL RELATIONSHIPS?. A relationship is proportional if each pair of data values are related in the same way, by multiplying by a factor. You can recognize a proportional relationship by looking at data, an equation, or a graph. To better understand proportional relationships…

LET’S BREAK IT DOWN!

Make muffins using a proportional relationship.

To make 1 dozen muffins, you need 2 eggs. If you want to make 2 dozen muffins, you need 4 eggs. To make 3 dozen muffins, you need 6 eggs. 1 times 2 is 2, 2 times 2 is 4, 3 times 2 is 6. The number of eggs is always 2 times the number of batches of muffins. This is called a proportional relationship. Now you try: How can you tell if the following data represents a proportional relationship? 1:3, 2:6, 3:9, 4:12

Make muffins using a proportional relationship. To make 1 dozen muffins, you need 2 eggs. If you want to make 2 dozen muffins, you need 4 eggs. To make 3 dozen muffins, you need 6 eggs. 1 times 2 is 2, 2 times 2 is 4, 3 times 2 is 6. The number of eggs is always 2 times the number of batches of muffins. This is called a proportional relationship. Now you try: How can you tell if the following data represents a proportional relationship? 1:3, 2:6, 3:9, 4:12

The constant of proportionality is the multiplication factor.

Adesina works different numbers of hours at a skating rink. The amount of money she makes for each number of hours she works is represented by this relationship: 1:$5, 2:$10, 3:$15, 4:$20, 5:$25. Is the relationship proportional? 1 times 5 is 5, 2 times 5 is 10, and so on. The number of dollars earned is always 5 times the number of hours worked. The relationship is proportional. The number that you always multiply by is called the constant of proportionality. The constant of proportionality of this relationship is 5. Now you try: What is the constant of proportionality for the following set of ratios? 2:14, 3:21, 4:28, 5:35

The constant of proportionality is the multiplication factor. Adesina works different numbers of hours at a skating rink. The amount of money she makes for each number of hours she works is represented by this relationship: 1:$5, 2:$10, 3:$15, 4:$20, 5:$25. Is the relationship proportional? 1 times 5 is 5, 2 times 5 is 10, and so on. The number of dollars earned is always 5 times the number of hours worked. The relationship is proportional. The number that you always multiply by is called the constant of proportionality. The constant of proportionality of this relationship is 5. Now you try: What is the constant of proportionality for the following set of ratios? 2:14, 3:21, 4:28, 5:35

You can identify if a relationship is proportional.

The following data shows the number of soccer games you played related to the number of goals you scored: 2:8, 3:12, 4:20, 5:36, 6:50. 2 times 4 is 8, and 3 times 4 is 12. But 4 times 4 is 16, not 20. And 5 times 4 is 20, not 36. You can't always multiply the number of games played by the same number to get the number of goals scored. This is a non-proportional relationship. Now you try: Identify if the following data represents a proportional relationship: 3:9, 5:15, 6:24, 8:32

You can identify if a relationship is proportional. The following data shows the number of soccer games you played related to the number of goals you scored: 2:8, 3:12, 4:20, 5:36, 6:50. 2 times 4 is 8, and 3 times 4 is 12. But 4 times 4 is 16, not 20. And 5 times 4 is 20, not 36. You can't always multiply the number of games played by the same number to get the number of goals scored. This is a non-proportional relationship. Now you try: Identify if the following data represents a proportional relationship: 3:9, 5:15, 6:24, 8:32

You can describe proportional relationships using equations.

Every kitten has 2 ears. You can write an equation to show how the number of kittens is related to the number of ears. Let x be the number of kittens and y be the number of ears. So, y=2x, since the number of ears is always twice the number of kittens. You can plug in any number of kittens for x to find the number of ears, y. For example, 5 kittens have y = 2 × 5 = 10 ears. Now you try: Write an equation to describe the relationship between the number of dogs and the number of legs in all.

You can describe proportional relationships using equations. Every kitten has 2 ears. You can write an equation to show how the number of kittens is related to the number of ears. Let x be the number of kittens and y be the number of ears. So, y=2x, since the number of ears is always twice the number of kittens. You can plug in any number of kittens for x to find the number of ears, y. For example, 5 kittens have y = 2 × 5 = 10 ears. Now you try: Write an equation to describe the relationship between the number of dogs and the number of legs in all.

You can recognize proportional relationships in equations and graphs.

Equations that represent proportional relationships are always in the form y=kx, where k is the constant of proportionality. That means that the relationship between x and y is always multiplicative, with nothing added or subtracted. Unlike y=2x, y=2x+4 and y=2x-5 do not represent proportional relationships. 4 is added or 5 is subtracted from the product. The graph of a proportional relationship is always a straight line that passes through the origin, (0, 0). Now you try: Identify which equation(s) represent proportional relationships: a) y=7.7x b) y=3x+5 c) y=13x

You can recognize proportional relationships in equations and graphs. Equations that represent proportional relationships are always in the form y=kx, where k is the constant of proportionality. That means that the relationship between x and y is always multiplicative, with nothing added or subtracted. Unlike y=2x, y=2x+4 and y=2x-5 do not represent proportional relationships. 4 is added or 5 is subtracted from the product. The graph of a proportional relationship is always a straight line that passes through the origin, (0, 0). Now you try: Identify which equation(s) represent proportional relationships: a) y=7.7x b) y=3x+5 c) y=13x

PROPORTIONAL RELATIONSHIP VOCABULARY

Proportional relationship

When two variables are always related in the same way through multiplication.

Constant of proportionality

The number that you always multiply by to define a proportional relationship.

Non-proportional relationship

When variables are not always related in the same way.

Equations

Two expressions that have the same value and are separated by an equal sign.

Coordinate Plane

A graph that uses two variables to describe the location of a point.

X-axis

The horizontal line on a graph.

The vertical line on a graph.

PROPORTIONAL RELATIONSHIP DISCUSSION QUESTIONS

Is y=2x+1 a proportional relation?

No. All proportional relationships are represented by equations that relate variables only through multiplication and are in the form y=kx, where k is any number. Since 1 is added in this equation, it is not proportional.